Casualty Actuarial Society Credentials (ACAS/FCAS) Exam 5 — Basic Techniques for Ratemaking and Estimating Claim Liabilities Syllabus

Exam 5 — Basic Techniques for Ratemaking and Estimating Claim Liabilities syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Exam 5 — Basic Techniques for Ratemaking and Estimating Claim Liabilities in Casualty Actuarial Society Credentials (ACAS/FCAS), not a summary of it.

1. 1

   Ratemaking Foundations

   3 topics

   • Insurance Data and Premium/Loss Concepts
     • Written, earned, and unearned premium
     • Paid, incurred, and reported losses
     • Exposure bases and policy aggregation
     • Calendar, accident, policy, and report year aggregation
   • The Fundamental Insurance Equation
     • Balancing premium, losses, expenses, and profit
     • Underwriting profit provision and target loss ratio
   • Premium Adjustments
     • On-leveling premium for rate changes (parallelogram method)
     • Premium trend and current rate level
2. 2

   Loss and LAE Development for Ratemaking

   3 topics

   • Loss Trending
     • Frequency and severity trend selection
     • Trend periods and leveraged trend on limits
   • Loss Development to Ultimate
     • Development triangles and age-to-age factors
     • Tail factor selection
   • Loss Adjustment Expenses
     • Allocated vs. unallocated LAE (ALAE/ULAE)
     • Including LAE in the rate indication
3. 3

   Overall Rate Indications and Rate Classification

   4 topics

   • Rate Indication Methods
     • Pure premium method
     • Loss ratio method
     • Reconciling the two approaches
   • Expense Provisions
     • Fixed vs. variable expenses
     • Permissible loss ratio and expense trend
   • Classification Ratemaking
     • Univariate and multivariate class analysis
     • Credibility-weighted relativities
     • Territorial and increased limits factors
     • Deductible and coinsurance pricing
   • Individual Risk Rating
     • Experience rating plans
     • Retrospective rating plans
4. 4

   Estimating Unpaid Claims (Reserving)

   4 topics

   • Reserving Fundamentals and Triangles
     • Components of unpaid claims (case, IBNR, IBNER)
     • Constructing and reading development triangles
     • Diagnostic ratios and data organization
   • Development-Based Methods
     • Chain ladder (development) method
     • Expected claims method
     • Bornhuetter-Ferguson method
     • Cape Cod (Stanard-Buhlmann) method
   • Frequency-Severity and Specialized Methods
     • Frequency-severity (Berquist-Sherman) techniques
     • Adjusting for changes in case reserve adequacy and settlement rates
   • Evaluating and Reconciling Estimates
     • Comparing method results and selecting ultimates
     • Monitoring actual vs. expected emergence
     • Estimating unpaid ULAE

Exam 5 — Basic Techniques for Ratemaking and Estimating Claim Liabilities flashcards for Casualty Actuarial Society Credentials (ACAS/FCAS)

20 of 51 cards from the Exam 5 — Basic Techniques for Ratemaking and Estimating Claim Liabilities deck — real questions with worked answers.

1. What is the difference between calendar year, accident year, policy year, and report year aggregation of insurance data?

   Calendar year (CY): transactions during a 12-month period regardless of accident/policy date — fixed once the year closes. Accident year (AY): groups losses by the date the loss occurred. Policy year (PY): groups premium and losses by the effective date of the policy generating them. Report year (RY): groups claims by the date the claim was reported (used for claims-made coverage).

2. Define written premium, earned premium, and unearned premium.

   Written premium is the total premium charged on policies written during a period. Earned premium is the portion corresponding to coverage already provided. Unearned premium is the portion for coverage not yet provided: $\text{UEP} = \text{WP} - \text{EP}$ (over the period, with beginning/ending reserves).

3. State the Fundamental Insurance Equation.

   $$\text{Premium} = \text{Losses} + \text{LAE} + \text{UW Expenses} + \text{UW Profit}$$ Ratemaking seeks to balance this equation prospectively so that premium adequately covers expected costs plus a target profit.

4. What are the four common methods for aggregating earned exposures, and which is generally most accurate?

   Calendar year, policy year, accident year, and report year. Policy year is the most accurate match of premium to the exposures that generated it, but it is the slowest to develop to maturity.

5. Define exposure (exposure base) and list the three desirable criteria for a good exposure base.

   An exposure is the basic unit of risk underlying the premium. A good exposure base should be: (1) proportional to expected loss, (2) practical (objective and inexpensive to obtain/verify), and (3) consistent with prior usage and historically established for the line.

6. What is the formula for pure premium (loss cost)?

   $$\text{Pure Premium} = \frac{\text{Losses}}{\text{Exposures}} = \text{Frequency} \times \text{Severity}$$ where $\text{Frequency} = \frac{\text{Claims}}{\text{Exposures}}$ and $\text{Severity} = \frac{\text{Losses}}{\text{Claims}}$.

7. Distinguish frequency and severity, and give their formulas.

   Frequency is the rate of claim occurrence: $\text{Frequency} = \frac{\text{Number of Claims}}{\text{Number of Exposures}}$. Severity is the average cost per claim: $\text{Severity} = \frac{\text{Losses}}{\text{Number of Claims}}$.

8. What is the difference between the loss ratio and the loss adjustment expense ratio?

   Loss ratio $= \frac{\text{Losses}}{\text{Earned Premium}}$. LAE ratio $= \frac{\text{LAE}}{\text{Losses}}$ (or to premium). The loss ratio measures pure loss cost relative to premium; the LAE ratio measures claim-settlement cost relative to losses.

9. Why is premium 'on-leveled' before being used in a rate indication?

   To restate historical premium to the rate level currently in effect, removing the distortion of past rate changes so that historical experience reflects what premium would be at today's rates. This makes the loss ratio comparison meaningful for projecting future rate needs.

10. Describe the parallelogram method (extension of exposures alternative) for on-leveling premium.

    The parallelogram method computes, for each calendar/policy year, the portion of premium earned under each historical rate level (the geometric areas of overlapping parallelograms). On-level factors are derived as the ratio of the current cumulative rate level index to the average rate level index for the period. It assumes policies are written uniformly over time.

11. What is the extension of exposures method for on-leveling premium, and when is it preferred over the parallelogram method?

    Extension of exposures re-rates each historical exposure using current rates to directly compute on-level premium. It is preferred when rates vary by class/territory (the parallelogram method assumes uniform writing and a single average rate change) and when detailed exposure data is available.

12. What is premium trend, and why is it applied separately from on-leveling?

    Premium trend captures changes in average premium per exposure due to shifts in the mix of business (distributional changes in amounts of insurance, deductibles, classes) not driven by rate changes. On-leveling captures rate changes; premium trend captures non-rate-change drifts in average premium level.

13. Distinguish the one-step and two-step premium trending approaches.

    One-step trending applies a single trend factor from the average written date of the historical period to the average written date of the future period. Two-step trending uses the latest actual average premium (current trend to end of historical data) then projects forward at a selected future (prospective) trend, accommodating a change in the trend rate.

14. What is loss trend and what are its two main components?

    Loss trend adjusts historical losses to the cost level expected during the future policy period. Components: (1) frequency trend (change in claims per exposure) and (2) severity trend (change in average cost per claim, driven by inflation, etc.). Total loss trend ≈ frequency trend × severity trend.

15. Define the trend period in loss trending and how it is measured.

    The trend period is the time from the average date of loss in the experience period to the average date of loss in the future (forecast) policy period. For an annual policy, the future average accident date is the midpoint of losses occurring on policies effective during the forecast year — roughly 1 year after the effective date midpoint.

16. How is the loss trend factor computed given an annual trend rate and a trend period?

    $$\text{Trend Factor} = (1 + t)^{n}$$ where $t$ is the annual trend rate and $n$ is the trend period in years. Frequency and severity trends may be applied separately and multiplied.

17. What is leveraged effect of inflation on excess (limited) layers?

    Uniform ground-up inflation increases losses in excess layers (above a fixed limit/deductible) at a rate higher than the underlying trend, because the fixed retention/limit absorbs a shrinking proportion of each loss. Thus excess-of-loss layers experience 'leveraged' trend greater than the base trend.

18. What is a loss development triangle and what does it display?

    A loss development triangle arrays cumulative (or incremental) losses by accident year (rows) and development age/maturity (columns). It shows how losses for each accident year grow as they mature, enabling estimation of development factors to ultimate.

19. How are age-to-age (link) development factors calculated from a cumulative triangle?

    For each pair of successive maturities: $$f_{i,j} = \frac{C_{i,j+1}}{C_{i,j}}$$ averaged across accident years (e.g., simple average, volume-weighted average, or average of latest N). Multiplying successive age-to-age factors gives age-to-ultimate factors (CDFs).

20. What is the cumulative development factor (CDF) and how is the tail factor handled?

    The CDF (age-to-ultimate) is the product of all remaining age-to-age factors from a given maturity to ultimate: $\text{CDF}_j = \prod_{k \ge j} f_k$. A tail factor extends development beyond the oldest observed maturity, often estimated from industry data, curve-fitting, or a benchmark when the triangle does not reach ultimate.

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